You'll want to use SD Alcohol to get that Aqua Velva sting that you're used to. Gin has a lot of other stuff in it.
The SD Alcohol is also called Denatured Alcohol, you can buy it in the hardware section of stores, usually by the paint stuff.
Link to the FDA page,
http://www.foodsafety.gov/~dms/cos-227.html
To prevent the ethyl alcohol in a cosmetic from being diverted illegally for use as an alcoholic beverage, it may be "denatured." This means that it contains an added "denaturant" that makes it undrinkable.
Denatured ethyl alcohol may appear in the ingredient listing under several different names. You may see the abbreviation SD Alcohol (which stands for "specially denatured alcohol"), followed by a number or a number-letter combination that indicates how the alcohol was denatured, according to the formulary of the United States Bureau of Alcohol, Tobacco, and Firearms (BATF). Among the specially denatured alcohols acceptable for use in various cosmetics are SD Alcohol 23-A, SD Alcohol 40, and SD Alcohol 40-B.
Just thought i would mention that.